/* mpfr_cbrt -- cube root function.

Copyright 2002, 2003, 2004, 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao projects, INRIA.

This file is part of the MPFR Library.

The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.

The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */

#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"

 /* The computation of y = x^(1/3) is done as follows:

    Let x = sign * m * 2^(3*e) where m is an integer

    with 2^(3n-3) <= m < 2^(3n) where n = PREC(y)

    and m = s^3 + r where 0 <= r and m < (s+1)^3

    we want that s has n bits i.e. s >= 2^(n-1), or m >= 2^(3n-3)
    i.e. m must have at least 3n-2 bits

    then x^(1/3) = s * 2^e if r=0
         x^(1/3) = (s+1) * 2^e if round up
         x^(1/3) = (s-1) * 2^e if round down
         x^(1/3) = s * 2^e if nearest and r < 3/2*s^2+3/4*s+1/8
                   (s+1) * 2^e otherwise
 */

int
mpfr_cbrt (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
  mpz_t m;
  mp_exp_t e, r, sh;
  mp_prec_t n, size_m, tmp;
  int inexact, negative;
  MPFR_SAVE_EXPO_DECL (expo);

  /* special values */
  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
    {
      if (MPFR_IS_NAN (x))
        {
          MPFR_SET_NAN (y);
          MPFR_RET_NAN;
        }
      else if (MPFR_IS_INF (x))
        {
          MPFR_SET_INF (y);
          MPFR_SET_SAME_SIGN (y, x);
          MPFR_RET (0);
        }
      /* case 0: cbrt(+/- 0) = +/- 0 */
      else /* x is necessarily 0 */
        {
          MPFR_ASSERTD (MPFR_IS_ZERO (x));
          MPFR_SET_ZERO (y);
          MPFR_SET_SAME_SIGN (y, x);
          MPFR_RET (0);
        }
    }

  /* General case */
  MPFR_SAVE_EXPO_MARK (expo);
  mpz_init (m);

  e = mpfr_get_z_exp (m, x);                /* x = m * 2^e */
  if ((negative = MPFR_IS_NEG(x)))
    mpz_neg (m, m);
  r = e % 3;
  if (r < 0)
    r += 3;
  /* x = (m*2^r) * 2^(e-r) = (m*2^r) * 2^(3*q) */

  MPFR_MPZ_SIZEINBASE2 (size_m, m);
  n = MPFR_PREC (y) + (rnd_mode == GMP_RNDN);

  /* we want 3*n-2 <= size_m + 3*sh + r <= 3*n
     i.e. 3*sh + size_m + r <= 3*n */
  sh = (3 * (mp_exp_t) n - (mp_exp_t) size_m - r) / 3;
  sh = 3 * sh + r;
  if (sh >= 0)
    {
      mpz_mul_2exp (m, m, sh);
      e = e - sh;
    }
  else if (r > 0)
    {
      mpz_mul_2exp (m, m, r);
      e = e - r;
    }

  /* invariant: x = m*2^e, with e divisible by 3 */

  /* we reuse the variable m to store the cube root, since it is not needed
     any more: we just need to know if the root is exact */
  inexact = mpz_root (m, m, 3) == 0;

  MPFR_MPZ_SIZEINBASE2 (tmp, m);
  sh = tmp - n;
  if (sh > 0) /* we have to flush to 0 the last sh bits from m */
    {
      inexact = inexact || ((mp_exp_t) mpz_scan1 (m, 0) < sh);
      mpz_div_2exp (m, m, sh);
      e += 3 * sh;
    }

  if (inexact)
    {
      if (negative)
        rnd_mode = MPFR_INVERT_RND (rnd_mode);
      if (rnd_mode == GMP_RNDU
          || (rnd_mode == GMP_RNDN && mpz_tstbit (m, 0)))
        inexact = 1, mpz_add_ui (m, m, 1);
      else
        inexact = -1;
    }

  /* either inexact is not zero, and the conversion is exact, i.e. inexact
     is not changed; or inexact=0, and inexact is set only when
     rnd_mode=GMP_RNDN and bit (n+1) from m is 1 */
  inexact += mpfr_set_z (y, m, GMP_RNDN);
  MPFR_SET_EXP (y, MPFR_GET_EXP (y) + e / 3);

  if (negative)
    {
      MPFR_CHANGE_SIGN (y);
      inexact = -inexact;
    }

  mpz_clear (m);
  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (y, inexact, rnd_mode);
}
